Experimental study on the vibration of an overhung rotor ...downloads.hindawi.com/journals/sv/2002/405928.pdf · bility of cracked rotors in the coupled vibration mode. The frequency

Shock and Vibration 9 (2002) 91–104 91IOS Press

Experimental study on the vibration of anoverhung rotor with a propagating transversecrack

S.A. Adewusi and B.O. Al-BedoorMechanical Engineering Department, King Fahd University of Petroleum and Minerals, P. O. Box 841, Dhahran31261, Saudi Arabia

Received 7 June 2000

Revised 30 July 2001

Abstract: This paper presents an experimental study on the dynamic response of an overhung rotor with a propagating transversecrack. The effects of a propagating transverse crack and side load on the dynamic response of an overhung rotor are investigated inorder to identify vibration signatures of a propagating crack in rotating shafts. Startup and steady state vibration signatures wereanalyzed and presented in the form of Bode plots, Frequency Spectrum Cascades, Frequency Spectrum Waterfalls and orbits. Thestartup results showed that crack reduces the critical speed and increases the vibration amplitude of the rotor system. It also excites2X vibration in the startup vibration signatures. The steady state results showed that the propagating crack produces changes invibration amplitudes of 1X and 2X vibration harmonics and excites 3X harmonic just before fracture. During crack propagation,1X amplitude may increase or decrease depending on the location of the crack and the direction of vibration measurement while2X amplitude always increases. The steady state vibration signal of a propagating crack also produces a two-loop orbit.

1. Introduction

The overhung rotor is important as it can be foundin many industrial turbo-machines in which the com-pressor and turbine has a single shaft, for an example,the turbocharger. Lateral forces can develop as a re-sult of misalignment, rotor weight, and fluid force influid handling machines and are usually in large scalethan the unbalance force. Although rotors are carefullydesigned for fatigue loading and high level of safetyby using high quality materials and precise manufac-turing techniques, catastrophic failures of rotors as aresult of cracks may still occur. Particularly, in highspeed rotating machines, in which the rotor is carry-ing disks, blades, gears, etc which are of considerableweight. Continuous operation of a cracked rotor willresult in crack propagation, which may result in a sud-den breakdown of the machine or one of its elements ifnot detected at an early stage. Although there are somereported effects of crack on vibration signals, little in-

formation is found on the effect of a propagating crackon vibration signals; this is the purpose of this work.

Due to the danger that the presence of a crack inrotor poses, research has been geared-up towards thedetection of crack in rotating machines using vibrationsignals. Many researchers [1–16] have modeled andstudied the dynamic response of cracked rotors usingdifferent approaches. Some used only theoretical mod-eling method, others combined both theoretical and ex-perimental methods and few used only experimentalmethod. Gasch [1] studied the stability behavior ofthe De-Laval rotor due to a crack and imbalance. Hisresults showed that the recognition of cracks is verydifficult because the significant double and triple fre-quency vibrations are only very slightly involved in thecrack response. Grabowski [2] used modal analysisto study the vibration behavior of a turbine rotor con-taining a transverse crack. He reported that the crackexcites 1X and 2X vibrations, which are independentof the out-of-balance but depend on the crack loca-

ISSN 1070-9622/02/$8.00 2002 – IOS Press. All rights reserved

92 S.A. Adewusi and B.O. Al-Bedoor / Experimental study on the vibration of an overhung rotor

(a)

(b)

Disk

BRG.Support 2

BRG.Support 1

Vert. Proximity probe

8 Kg

ElectricMotor

Hor. Proximity Probe

RollerElementBearing

Surfacecrack

30o

4mm

10 mm

Fig. 1. Experiment rig. (a) Schematic diagram for Overhung rotor arrangement. (b) Crack geometry.

Table 1Summary of the experimental results

Description Steady state Start upY probe X probe Critical speeds (rpm)

1X (mil) 2X (mil) 1X (mil) 2X (mil) Y X

Un-cracked Shaft with hanging side load 2.080 0.025 0.694 0.231 4025 1785of 8 kg (3500 rpm)

1st Cracked Shaft with 4 mm notch with 0.617 2.130 0.720 2.850 4010 1728hanging side load of 8 kg (3500 rpm) (−70.3%) (very high) (+3.74%) (high)

2nd Cracked Shaft with 4 mm notch with 4.990 1.820 3.140 5.860 3750 1720hanging side load of 8 kg (3500 rpm) (+139.9%) (high) (+244.6%) (very high)

tions. Dimarogonas and Paipetis [3] developed a rela-tionship between crack depth and rotor local flexibility.Imam et al. [4] used a 3-D finite element method anda nonlinear rotor dynamics to model a cracked rotorsystem and developed an on-line rotor crack detectionand monitoring system. Histogram signature analysis,which is the FFT of the difference between the aver-aged vibration signals of cracked and un-cracked shaftwas used. Experiment results showed 1X and 2X vi-bration peaks. Inagaki et al. [5] utilized the iterative nu-merical calculation (transfer matrix) method to analyzetransverse vibrations of a general cracked-rotor bear-ing system and an experiment was used to validate theresults. The experimental results showed 1X and 2Xvibration responses under mutual influences betweengravity, imbalance and their phase relations, and vibra-tion mode characteristics at the rotating speed. Thework of Dirr and Schmalhorst [6] was comprehensive.

They used vibration measurement method and poten-tial difference method of fatigue crack measurementto study the shape of cracks at different depth duringcrack propagation in a rotating shaft. The FFT of ex-perimental vibration signals showed 1X and 2X. 3DFinite Element crack model was also used to study thebending stress distribution near the crack tip. Mayesand Davies [7] analyzed the response of a multi-rotor-bearing system with a transverse crack using a linearrotor dynamic computer program. The results weresupportedby experimentalwork using a test rig to studythe effect of dynamic bending moments and rotor run-ning speed on crack depth. Bently and Bosmans [8]used experimental set-up to study a cracked rotor modelof a Reactor Coolant Pump using an overhung rotor.The results showed variations in the amplitude of the2X vibration and an orbit with two loops due to crackpropagation. Wauer [9,10] carried out a comprehensive

S.A. Adewusi and B.O. Al-Bedoor / Experimental study on the vibration of an overhung rotor 93

(b) Horizontal direction

side load(a) Vert ical direction

Fig. 2. Bode plots of startup data for un-cracked shaft with 8 kg vertical hanging side load.

literature survey on the state-of-the-art of the dynamicsof cracked rotors. He also modeled and formulated thegoverning dynamic equations of a cracked Timoshenkorotor, which is flexible in extension and torsion. Heused the Galerkin’s method to reduce the equations ofmotion. The torsional vibration of a circular shaft witha circumferential crack was studied. Collins et al. [11]studied a cracked Timoshenko rotor by solving the six-coupled equations obtained by Wauer [9,10]. The fre-quency spectrum of the rotor response to a periodicaxial impulse was also studied. The results showedan increase in the coupling between axial, torsionaland transverse vibration. Theoretical and experimentalstudy of the on-line crack detection for turbo-generatorrotors was presented by Diana et al. [12]. The effectsof thermal gradient were accounted for in the diagnos-

tic program, using probability evaluation. The differ-ence between the current vibration and the previous vi-bration was used to calculate the vibration forces. 1Xand 2X vibration frequency components were reported.Dimarogonas and Papadopoulas [13] studied the sta-bility of cracked rotors in the coupled vibration mode.The frequency spectra of the vibration signal of a 300MW steam turbine showed high 2X, 1/2X and 1/4Xvibration components that suggested the existence ofdeep crack. Meng and Hahn [14] analyzed a crackedJeffcott rotor theoretically and numerically. WU andHuang [15] studied the dynamic response of a rotorwith a transverse crack by numerically solving the dy-namic equations of a cracked rotor model. FFT of theresponse at various speeds, crack depths and crack lo-cations showed 1X and 2X harmonics. Floquet theory


(a) Vertical direction


Fig. 3. Frequency cascades of the startup data for un-cracked shaft with 8 kg hanging side load.

and multiple scales methods were also used to studythe stability of the cracked shaft system. Zheng [16]numerically studied the vibration of rotor system witha switching crack. He suggested the use of featuresother than 1X and 2X harmonics for crack detection.The Gabor analysis of the vibration signals, after 1Xand 2X have been removed, showed the presence oftransient signals.

Attention has been focused on the study of a sim-ply supported cracked rotor. All the works citedabove, with the exception of the work of Bently andBosmans [8], were on a simply supported rotor. Fur-thermore, majority of the results showed that crack ex-cites 1X and 2X vibration harmonics at steady state.However, imbalance can produce 1X harmonic whilemisalignment, asymmetry and looseness of bolts andnuts can also produce 2X vibration. Similarly, a change

in the critical speed of a rotating machine may be causedby other machine faults like looseness and wear. There-fore, in accordance with the suggestion of Zeng [16],more than one vibration feature should be used to char-acterize the presence of a crack in rotors to avoid wrongdiagnosis. This paper uses four different vibration fea-tures to study the vibration of an overhung rotor witha transverse propagating crack and side load. Thesefeatures are Frequency Cascades and Frequency Wa-terfalls that give information on frequency and time ofthe vibration signal, Bode plots and orbits.

2. Experimental setup

The equipment used for the experiment include aRotor Kit, Rotor Kit Motor Speed Control, Data Ac-




Fig. 4. Frequency waterfalls of steady state data for un-cracked shaft with 8kg hanging side load.

quisition Interface Unit (DAIU-208P) with accessories,Oscilloscopes, Personal Computer (PC), Eddy CurrentDisplacement/proximity Probes, Automated Diagnos-tics for Rotating Equipment (ADRE) for Windows Soft-ware and shafts. The schematic diagram of the ex-periment test rig is set up as shown in Fig. 1(a). Theproximity probes are fixed on rigid supports 4 cm fromthe bearing supports and are connected via auxiliarycomponents to Oscilloscopes to observe the amplitude-time waveforms and orbits of the vibration signals. Theprobes are also connected to the DAIU-208P, whichis in turn connected to the PC. The DAIU operationis controlled by the ADRE for Window Software tocollect, store and analyze vibration data to obtain Or-

bits, Bode plots, Frequency Spectrum Waterfall, andFrequency Spectrum Cascades.

The shaft material is made of ductile steel bar AISI4140. The shaft has the following dimensions andproperties: 10 mm diameter, 540 mm length, mass perunit length of 0.72 kg/m, Young’s Modulus of 200 GPa.Two disks each of mass 0.8 kg and a hanging sideload of mass 8 kg were fitted on the shaft as shown inFig. 1(a). The 8 kg hanging side load was applied toproduce bending stress on the crack and aid crack prop-agation. The 8 kg it is attached to the roller elementbearing on the shaft through an inelastic string of diam-eter 2 mm. The shafts are supported in self-lubricatingsleeve bearings. Three shafts are machined one with-out crack and the other two with 4 mm depth v-notch


Fig. 5. Orbit for un-cracked shaft with 8 kg vertical hanging side load.

surface crack. The crack angle is 30◦ and the CrackTip Open Displacement (CTOD) was measured withthe optical microscope and was found to be 0.117 mm.Figure 1(b) shows the crack geometry.

Three experiments were carried out. It was ensuredthat the shaft centerline was perfectly aligned with theElectric Motor rotation axis to eliminate response dueto misalignment. The first experiment was for the un-cracked shaft with the disks and 8 kg hanging side loadlocated at 7 cm and 13 cm from the Bearing Support 1,respectively while the distance between the bearingsupports was 39 cm. The second experiment consistedof the first cracked shaft with 4 mm depth v-notchsurface crack located at 1.5 cm from Bearing Support 1,Fig. 1(a). The locations of the disks, 8 kg hanging sideload, and bearing supports are the same as those for thefirst experiment. In the third experiment, the secondcracked shaft with the 4 mm depth v-notch surfacecrack located at 3.5 cm from the Bearing Support 1was used. The disks and 8 kg hanging side load arelocated at 10 cm and 16 cm from the Bearing Support 1,respectively while the distance between the bearingsupports was 39 cm. It should be noted that the 8 kg sideload was attached to the shaft for the three experiments.This enables the effects of a propagating crack to bestudied since the effect of the 8kg load is common toall set-ups.

The startup and steady vibration signals for each ex-periment are taken and analyzed and the results are pre-sented and discussed in the following section. The vi-

bration signals in both the vertical and horizontal direc-tions measured by the proximity probes located 4 cmto Bearing Support 1 are considered. The ramp rate forthe startup or run-up experiments was 10000 rpm perminute and vibration data are taken every 15 rpm in-crease in the speed of the rotor. The steady state speedfor the steady state experiments was 3500 rpm.

3. Results and discussions

Startup vibration signals were presented in the formof Bode plots, which give information on the criti-cal speed of the rotor system and Frequency Cascadesthat give information on the vibration harmonics in thestartup signals. Steady state vibration signals were pre-sented in the form of Frequency Waterfalls, which giveinformation on the harmonic components and Bodeplots that give informationon the movementof the shaftcenter. The resonance speed corresponding to the crit-ical speed of the rotor system is shown on each Bodeplot at the right hand top corner. The vertical overhungside load was attached to the rotor with a thick string(Fig. 1(a)) to aid crack propagation. This arrangementmakes the setup to have two degree of freedom in thevertical direction; this is clearly shown in the Bode plotsin form of a resonance point at lower speed of 540 rpm,in the vertical Bode plots, Figs 2(a) and 6(a). It shouldbe noted that the resonance frequency of the loadingsystem is very small. Therefore at high frequencies




Fig. 6. Bode plots of startup data for the 1st shaft with 4 mm notch crack and 8 kg vertical hanging side load.

in order of 3500 rpm (the steady state speed), the 8kgmass will not actively participate in the dynamics of therotor system and can be neglected. This resonance isignored in the discussion of the results. The amplitudevalue in mil for 1X or 2X vibration harmonic is shownat the down right hand corner of every frequency wa-terfall. Table 1 summarizes the amplitudes of 1X and2X harmonics for all steady state experiments.

3.1. Un-cracked shaft

Figures 2 and 3 represent the startup results for theun-cracked shaft with 8 kg hanging side load. Fig-ures 2(a) and (b) are Bode plots of the startup vibra-tion signals in the vertical and horizontal directions,

respectively. Figure 2(a) shows that the first rotor crit-ical speed in the vertical direction is around 4000 rpmwhile in the horizontal direction, Fig. 2(b), the first crit-ical speed is around 1800 rpm. This asymmetry is duemainly to the side load that stiffens the rotor system inthe vertical plane as it forces the shaft to be touchingthe sleeve bearing at the upper and lower sides con-tinuously. Other important observation in Fig. 2(b) isthe second resonance peak, which is probably the rotorsecond critical speed in the horizontal direction. Fig-ures 3(a) and (b) are the Frequency Cascades of thestartup signals in the vertical and horizontal directions,respectively. The horizontal proximity probe shows 2Xvibration harmonics at and above a speed correspond-ing to the second critical speeds shown in Fig. 2(b).




Fig. 7. Frequency cascades of startup data for the 1st shaft with 4 mm notch crack and 8 kg vertical hanging side load.

This suggests that the second mode vibration is excitedin the horizontal direction with small amplitude com-pared with the first 1X vibration. It should be noted thatthere was no 2X harmonic in the horizontal directionbefore the second critical speed was reached.

Figures 4 and 5 present the steady state results forthe un-cracked shaft with 8 kg vertical hanging sideload. Figures 4(a) and (b) show the Frequency Wa-terfall in the vertical and horizontal directions, respec-tively. Figure 4 shows that the vibration amplitude isgreater in the vertical direction with 1X dominating.2X and 3X vibration harmonics are also present but theamplitude of 3X is greater than that of 2X. The vibra-tion in the horizontal direction is rich in harmonics. 1X,

2X, 3X, 4X and higher harmonics are present. Thereis also an unsteady sub-harmonic in the horizontal sig-nal. The harmonics other than 1X can be attributed tothe effect of the side load, which produced asymmetryin the shaft system. The unsteady behavior shown inFig. 4(b) was probably due to temperature dependenceof the equivalent stiffness and damping characteristicsof the bearings. Figure 5 represents the orbit of thesteady state signal of the un-cracked shaft and it showsthat the movement of the shaft centerline is greater inthe vertical direction despite the restriction imposed bythe side load. This behavior is due to the fact that thevertical side load increased the static deflection of theshaft in the vertical direction.




Point of fracture

Point of fracture

Fig. 8. Frequency waterfalls of steady state data for the 1st shaft with 4 mm notch crack and 8 kg vertical hanging side load.

3.2. Cracked shaft

Figures 6 and 7 present startup results for the 1stcracked shaft with 4 mm notch and 8 kg hanging sideload. The startup data for this shaft and the un-crackedshaft were taken more than one time and averaged val-ues of critical speeds are presented in Table 1. The re-peated startup experiment for the cracked shaft causedcrack propagation and the shaft fractured after sometime when left to run at steady state as shown in Fig. 8.Figure 6 shows the Bode plots of startup signals in thevertical and horizontal directions. The crack reduced

the critical speed of the rotor system and increased am-plitudes of vibration in both directions when Figs 6 and2 are compared. These results are consistent with theresults reported by Dimarogonas and Paipetis [3]. Fig-ure 7 represents the Frequency Cascades of the startupsignals in both the vertical and horizontal directions.It can be seen in Fig. 7 that crack excited 2X vibra-tion harmonic throughout the transient period in boththe vertical and horizontal directions unlike what is ob-served in Fig. 3 where 2X occurred only in the hori-zontal direction and at a speed close to and above thesecond critical speed in the horizontal direction. See


Fig. 9. Orbit of steady state data for the 1st shaft with 4 mm notch crack and 8 kg vertical hanging side load before the shaft fractured.

also Fig. 11 for the second cracked shaft. This is an im-portant feature that can be used to identify the presenceof crack in rotors in addition to the decrease in criticalspeed during startup.

Figures 8 and 9 show the steady state results for the1st rotor with 4 mm v-notch crack. Figure 8 is the Fre-quency Waterfalls for the vertical and horizontal vibra-tion signals during crack propagation and shaft fracture.1X and 2X vibration harmonics are very prominentin both directions. The 2X amplitude is greater than1X amplitude and 2X amplitude increased as the crackpropagated till fracture occurred. This result agreeswith the results reported by Gasch [1], Grabowski [2],Imam et al. [4], T. Inagaki et al. [5], G. Dirr and Shmal-horst [6], Davies and Mayes [7] and Diana et al. [12].A small 3X vibration harmonic was excited at a laterstage of crack propagation just before fracture occurred.Figure 9 represents the orbit of the cracked shaft dur-ing crack propagation. Two-loop orbit similar to thatreported by Bently and Bosmans [8] is obtained.

Figures 10 and 11 show the startup results for the2nd rotor with 4 mm v-notch crack. In this arrange-ment, the crack, disks and hanging side load were lo-cated further away (10 cm and 16 cm respectively) fromthe Bearing Support 1 than for the 1st cracked rotor(7 cm and 13 cm). In this arrangement, the resonancebandwidth as shown in Fig. 10(a) is small comparedwith Figs 2(a) and 6(b). The decrease in the critical

speed and increase in vibration amplitude are greatercompared with the 1st cracked rotor. This is expectedsince the bending moment due to the hanging side loadand disks on the crack is greater than that for the 1stcracked shaft. Gasch [1] and Meng and Hahn [14] havereported that the change in shaft stiffness and dynamicresponse of a shaft-bearing system depends on both thecrack depth and crack location. Figure 11 shows theFrequency Cascades of the 2nd cracked rotor. 2X vi-bration harmonic is present in both directions and issimilar to Fig. 6. This shows that crack excites 2Xharmonic during startup.

Figure 12 represents the Frequency Waterfalls of thesteady state signals of the 2nd cracked rotor. 1X and2X harmonics are very prominent, their amplitudesincreased as the crack propagated. 1X amplitude isgreater in the vertical direction while 2X amplitude isgreater in the horizontal direction. 3X vibration har-monic was excited at a later stage of crack propaga-tion. Figure 13 shows the orbit of the steady state vi-bration signal of the 2nd cracked rotor, wherein a dis-torted two-loop orbit is formed. The distortion of theorbit can be attributed to higher wobbling effects of thehanging side load and disks as a result of greater overoverhanging length.

Table 1 summarizes the experimental results for theun-cracked and the cracked rotors. The table shows 1Xand 2X vibration amplitudes measured in the vertical



ad.


Fig. 10. Bode plots of startup data for the 2nd shaft with 4 mm notch crack with 8 kg vertical hanging side load.

and horizontal directions and their percentage change.The averaged critical speeds for the un-cracked rotorand the cracked rotors are also presented in the tablefor comparison.

4. Conclusions

Experimental results on the dynamic response of anoverhung rotor with 4 mm v-notch propagating trans-verse crack is presented. Since the machine historyis important in fault detection in rotating machines,

startup vibration signals of un-cracked and crackedshafts were presented in the form of Bode plots andFrequency Cascades for comparison. Steady state datafor the un-cracked and cracked rotors were presentedin the form of Frequency Waterfalls and orbits. Thestartup results showed that crack reduces the criticalspeed and increases the vibration amplitude of the rotorsystem and also excites 2X vibration harmonic. Thesteady state results showed that a propagating crackproduces changes in vibration amplitudes of 1X and2X harmonics and excites 3X harmonic at a later stageof crack propagation. During crack propagation, 1X




Fig. 11. Frequency cascades of startup data for the 2nd shaft with 4 mm notch crack and 8 kg vertical hanging side load.

amplitude may increase or decrease depending on thelocation of the crack while 2X amplitude always in-creases as the crack propagates. The steady state vibra-tion signal of a propagating crack also produces a two-loop orbit. Changes in amplitudes of 1X and 2X vibra-tion harmonics at a constant running speed is an impor-tant feature that distinguishes a propagating crack fromimbalance and misalignment. These relative changesshould be monitored and not their absolute values. Theresults obtained suggest that the dynamic response ofan overhung rotor to a propagating crack is similar tothe dynamic response of a simply supported rotor to apropagating crack. Further studies using mathematicalmodeling to quantify the rate of change in 2X vibra-tion signal as related to the changing crack depth isrecommended.

Acknowledgement

The authors appreciate the support of King FahdUniversity of Petroleum and Minerals, Dhahran, SaudiArabia. The support of Dr. Don Bently of BentlyNevada Corporation, Minden-Nevada, USA is also ac-knowledged and appreciated.

References

[1] R. Gasch, A Survey of the Dynamic Behavior of a SimpleRotating Shaft with a Transverse Crack,Journal of Sound andVibration 160(2) (1993), 313–332.

[2] B. Grabowski, The Vibrational Behavior of a Turbine RotorContaining a Transverse Crack,Transactions of the ASME 102(1980), 141–146.




Fig. 12. Frequency waterfalls of steady state data at 3500 rpm for the 2nd shaft with 4 mm notch crack with 8 kg vertical hanging side load.

[3] A.D. Dimarogonas and S.A. Paipetis,Analytical Methods inRotor Dynamics, Applied Science Publishers, London, 1983.

[4] Imam, S.H. Azzaro, R.J. Bankert and J. Scheibel, Develop-ment of an On-Line Rotor Crack Detection and MonitoringSystem,Journal of Vibration, Acoustics, Stress, and Reliabil-ity in Design 111 (1989), 241–250.

[5] T. Inagaki, H. Kanki and S. Shiraki, Transverse Vibrations ofa General Cracked Rotor Bearing System,Journal of Mechan-ical Design 104 (1982), 345–355.

[6] B.O. Dirr and B.K. Schmalhorst, Crack Depth Analysis ofA Rotating Shaft by Vibration Measurements,11th ASMEConference on Mechanical Vibration and Noise, Boston, 1987,pp. 607–614.

[7] I.W. Mayes and W.G.R. Davies, Analysis of the Response ofa Multi-Rotor-Bearing System Containing a Transverse Crackin a Rotor,Journal of Vibration, Acoustics, Stress, and Relia-bility in Design 106 (1984), 139–145.

[8] D.E. Bently and R.F. Bosmans,Case Study of Shaft CrackFailure, Orbit, 1989.

[9] J. Wauer, On the Dynamics of Cracked Rotors: A LiteratureSurvey,Applied Mechanics Review 43(1) (1990), 13–17.

[10] J. Wauer, Modeling and Formulation of Equations of Motionfor Cracked rotating Shafts,International Journal of SolidsStructures 26(8) (1990), 901–914.

[11] K.R. Collins, R.H. Plaut, C.E. Via and J. Wauer, Detection ofCracks in Rotating Timoshenko Shafts using Axial Impulses,Transactions of the ASME 113 (1991), 74–78.

[12] G. Diana, N. Bachschmid and F. Angeli, An On-Line CrackDetection Method for Turbogenerator Rotors,Proceedingsof International Conference on Rotordynamics, Tokyo, 1986,pp. 385–390.

[13] A.D. Damarogonas and C.A. Papadopoulas, Vibration ofCracked Shaft in Bending,Journal of Sound and Vibration 91(1983), 583–593.

[14] G. Meng and E.J. Hahn, Dynamic Response of a CrackedRotor With Some Comments on Crack Detection,Journal ofEngineering for Gas Turbine 119 (1997), 447–455.


(b) During crack propagation.

(a) Before crack propagation

Fig. 13. Orbit of steady state data at 3500 rpm for the 2nd shaft with 4 mm notch crack and 8 kg vertical hanging side load during crackpropagation.

[15] M.-C. Wu and S.-S. Huang, In-Plane Vibration and CrackDetection of a Rotating Shaft-Disk Containing a TransverseCrack,Journal of Vibration and Acoustics 120 (1998), 551–555.

[16] G.T. Zheng, Vibration of a Rotor System with a Switching

Crack and Detection of the Crack,Journal of Engineering forGas Turbine 120 (1998), 149–154.

[17] L.R.K. Nilson, On the Vibration Behavior of A Cracked Rotor,IFToMM Rotordynamics Problems in Power Plants Confer-ence Proceedings, Rome, Sep 1982, pp. 512–524.

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Experimental study on the vibration of an overhung rotor ...downloads.hindawi.com/journals/sv/2002/405928.pdf · bility of cracked rotors in the coupled vibration mode. The frequency